According to the Centers for Medicare & Medicaid Services, 21% of nursing homes in the United States received five stars in overall ratings on a scale of 1 to 5. A random sample of seven nursing homes was selected. What is the mean of this distribution?

Question

Quizplus · Accepted Answer

The mean of a binomial distribution is given by $ \mu = np $, where $ n $ is the number of trials (in this case, 7 nursing homes) and $ p $ is the probability of success (in this case, 0.21, or 21% of nursing homes receiving five stars). Thus, $ \mu = 7 \times 0.21 = 1.47 $.